Erik Kusch, PhD Student
Department of Biology
Section for Ecoinformatics & Biodiversity
Center for Biodiversity Dynamics in a Changing World (BIOCHANGE)
Aarhus University
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 1
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 2
What if there is heterogeneity in measurement error?
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 3
If in doubt, use a DAG!
Conditional probability gives us a
generative model from the DAG.
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 4
Just need to add priors, in this case.
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 5
One D_true value for each state
in the data set
D_sd is a variable in the data set!
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 6
Observed divorce rate (D)
Modelled true divorce rate
(D_true)
Shrinkage
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 7
So, what if the predictors have some error?
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 8
More priors!
But… M and A are related. Can’t we use that
information as a prior for M?
This model is not optimal. We can fix this by
putting the entire DAG into the model.
See chapter exercises
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 9
Observed divorce
rate (D)
Modelled true
divorce rate (D_true)
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 10
”Grown up measurement error is
missing data”.
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 11
H⊥D|A
”When is S->H* a good approximation
of S->H?.
H⊥D
H=f(D)
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 12
We will first talk through
some DAGs for the
other types of
missingness.
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 13
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 14
Missing Completely At Random
Missingness is fully random.
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 15
Missing At Random
Something causes missingness.
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 16
Missing Not At Random
Missingness caused by variable itself or by latent variable.
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 17
Observed and
unobserved values
Prior for unobserved B-values /
Likelihood for observed B-values
ulam() detects NA values automatically.
07/05/2021
[Study Group] Bayesian Statistics with the Rethinking Material 18
